@Crapoly,
I don't think it's too soon if you're feeling this way.
As for asking her out, why not start with coffee? It's a lot less of a commitment and it goes faster. Hence if it doesn't go well, everyone gets to ditch a lot more quickly. So, something like,
"Hi, Carol (or whatever her name is)
, do you want to get coffee sometimes? The Starbucks on 10th Street has great blueberry muffins." And of course change the details as needed.
Talk, laugh, have fun and seal the deal at the end by asking,
"I've had a really great time. Would you like to have dinner with me tomorrow night?"
A two-step process works rather neatly as the first part gives everyone a chance to back out if necessary. Sometimes things look good on paper, as it were, but you find yourself checking your watch every five seconds. The second meeting is a much more clearly-presented date, and if she asks (for either meeting, I might add), "Is this a date?" you can answer with something like, "I'd like it to be."